I think 1971 but Letter will tell you for sure
Nice gun! According to Standard Catalog of Smith & Wesson, 4th Edition, The M letter prefix for Model 34-1 for year 1971 started with M 30001, and 1973 started with M60001.
I had two Model 34-1's both great guns but gone now. One was serial number M51960 and shipped in 1972, the other was s/n M77380 and shipped in Feb 1975. I can only find a couple pics of my 1975 one.
If you join the SWCA (Smith & Wesson Collectors Association) you have access to Dr. Roy Jinks and can ask him for the ship date (Month & Year) of your serial number. Alternatively, you can send to the SWHF (Smith & Wesson Historical Foundation) for a Letter of Authentication. I think the cost of the Factory Letter is $100 but I may be in error. The cost of asking Dr. Roy for the ship date is free for Members.
Bottom line? I'm guessing you have a 1971 shipment but I could be off by years...because S&W doesn't really ship in numerical sequence with whatever date the frame was stamped with a serial number (the so called manufacture date). This is why Collectors use the ship date as the birth date of any S&W.